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Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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Explore the relationship between simple linear functions and their graphs.

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Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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By selecting digits for an addition grid, what targets can you make?

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How many solutions can you find to this sum? Each of the different letters stands for a different number.

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Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

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Find the values of the nine letters in the sum: FOOT + BALL = GAME

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The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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Use your knowledge of place value to try to win this game. How will you maximise your score?

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Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

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Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

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Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

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Where should you start, if you want to finish back where you started?

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Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

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The Number Jumbler can always work out your chosen symbol. Can you work out how?

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Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

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Can you work out some different ways to balance this equation?

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Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

This article for primary teachers expands on the key ideas which underpin early number sense and place value, and suggests activities to support learners as they get to grips with these ideas.

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Have a go at balancing this equation. Can you find different ways of doing it?

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

This article develops the idea of 'ten-ness' as an important element of place value.

One of the key ideas associated with place value is that the position of a digit affects its value. These activities support children in understanding this idea.

These tasks will help learners develop their understanding of place value, particularly giving them opportunities to express numbers as amounts.

More upper primary number sense and place value tasks.

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What happens when you add a three digit number to its reverse?

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Try out some calculations. Are you surprised by the results?

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Try out this number trick. What happens with different starting numbers? What do you notice?

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Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

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Can you replace the letters with numbers? Is there only one solution in each case?

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32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.

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Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

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Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

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What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

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Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

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Find the sum of all three-digit numbers each of whose digits is odd.

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This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .

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A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?

In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.